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JEE Main202131 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The distance of the point ( - 1 , 2 , - 2 ) from the line of intersection of the planes 2 x + 3 y + 2 z = 0 and x - 2 y + z = 0 is :

Options

  1. A1 2
  2. B42 2
  3. C5 2
  4. D34 2

Correct answer

D. 34 2

Step-by-step solution

P 1 :   2 x + 3 y + 2 z = 0 ⇒   n 1 → = 2 i ^ + 3 j ^ + 2 k ^ P 2 :   x - 2 y + z = 0 ⇒     n 2 → = i ^ - 2 j ^ + k Let, line L is the line of intersection of P 1 & P 2 The direction vector of the line is r → = n → 1 × n → 2 = 7 i ^ - 7 k ^ DR's of L are 1 , 0 , - 1 and origin is a common point on both the planes ⇒ Equation of L :   x 1 = y 0 = z - 1 = λ Now, DR's of P Q → = λ + 1 ,   - 2 ,   2 - &#9

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